G.CO.A.2 STUDENT NOTES & PRACTICE WS #3/#4 – geometrycommoncore.com 1

An ISOMETRIC TRANSFORMATION (RIGID MOTION) is a transformation that preserves the distances and/or angles between the pre-image and image.

In simpler words…. An isometric transformation maintains the shape and size of the pre-image.

Example #1 Example #2 Example #3 D I L' C' J I' L B' J' C E E' D' F F' M M' B H K' H' K

Rotate (Turn) Translate (Slide) Reflection (Flip)

Rotations, Translations and Reflections are examples of isometric transformations.

A NON-ISOMETRIC TRANSFORMATION (NON-RIGID MOTION) is a transformation that does not preserve the distances and angles between the pre-image and image.

Example #1 Example #2 Example #3 C' F L M

C E K N D' G F' D L' M'

E' G' B B' K' N'

Dilation (Proportional) Stretch (Not Proportional) Stretch (Not Proportional)

Stretch – Where one dimension’s scale factor is different than the other dimension’s scale factor. Examples #2 and #3 represent stretches. A stretch definitely distorts the shape making it a NON-ISOMETRIC transformation.

Dilation – Where both dimension’s scale factors is the same. The shape is proportional, not identical. Dilation changes the size of the shape making it a NON-ISOMETRIC transformation.

There are many ways to distort a shape but these two are the most popular types.

1. Circle which of the following are isometric transformations? (there may be more than 1 answer)

Pre-Image a) Image b) Image c) Image 2. Use the previous example to determine which transformation took place, circle the answer.

Pre-Image a) Reflection b) Reflection c) Reflection Translation Translation Translation Rotation Rotation Rotation Dilation Dilation Dilation Stretch Stretch Stretch Other Other Other

3. Circle which of the following are isometric transformations? (there may be more than 1 answer)

Pre-Image a) Image b) Image c) Image

4. Use the previous example to determine which transformation took place, circle the answer.

Pre-Image a) Reflection b) Reflection c) Reflection Translation Translation Translation Rotation Rotation Rotation Dilation Dilation Dilation Stretch Stretch Stretch Other Other Other

5. Determine the coordinates of the image, plot the image and determine if it is an isometric transformation or not. PRE-IMAGE Transformation COORDINATES PLOT THE IMAGE a) Pre-Image Points Image Points B4 4 A (-1,1) A’ (_____,_____) 2 2 B (0,4) B’ (_____,_____) A -5 C5 -5 5 C (4,1) C’ (_____,_____) -2 Isometry? Yes or No -2 Coordinate Rule -4 -4 (x,y)  (x, -y) Transformation Type: ______

6. Determine the coordinates of the image, plot the image and determine if it is an isometric transformation or not. PRE-IMAGE Transformation COORDINATES PLOT THE IMAGE G.CO.A.2 STUDENT NOTES & PRACTICE WS #3/#4 – geometrycommoncore.com 3

a) Pre-Image Points Image Points 4B 4 A (0,0) A’ (_____,_____) 2 2 B (1,3) B’ (_____,_____) -5 A 5 C C (5,0) C’ (_____,_____) -5 5 -2 Isometry? Yes or No -2 Coordinate Rule -4 -4 (x,y)  (x, -2y) Transformation Type: ______